It has proven problematic that the worn material to be removed that is present on the wheel tread surface and wheel flange surface has different thicknesses, and therefore different demands are placed on the cutting insert, the cutting depth thereof and the chip formation. This concerns in particular the transition from the wheel tread surface to the wheel flange surface, as chip control is particularly difficult in this region. Moreover, it is not always possible to remove all of the material in one pass, so that withdrawal and repositioning of the cutting insert is required in order to machine first the wheel tread surface and then the wheel flange surface. One or more complete cutting passes are possible as well.